Percolation and fracture in disordered solids and granular media: Approach to a fixed point

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Abstract
We argue that there exist universal fixed points (FPs) that classify the universality classes of fracture processes in disordered media. As a system approaches its macroscopic failure point, the ratio of its elastic moduli appears to approach a universal value, independent of microscopic features of the system. We suggest that there are two such FPs: one describes systems that are under a uniform external load and in which fracture does not take place at random, but depends on the stress field in the system, while the other describes systems in which fracture accumulates at random and is identical with the FPs of elastic percolation networks. Experimental data on fractured rocks appear to support this.